Download Math 240 – Mrs

LAMC
Review
Math 125
Exam 4
Chapter 6 and 7
1. Simplify the following, if possible.
a.
3
8
1 
b.
3
c.
8 
4
d.
81
2. Simplify the following. All variables represent positive values. Leave the answers in rational exponent
form.
1
a.
 4
5

2
5
4
1
2
b. 16 

c. 4x x
1 2 2


2
d.  49x y 3  


2
3
3. Simplify the following. All variables represent positive values.
a.
12x 8
b.
3
81ab5
c.
c.
5 18
3 12
4. Perform the addition, subtraction, or multiplication. Simplify your answers.
a. 3 50  2 32  4 18
c.
e.
b.
45x 3  18x 2  50x 2  20x 3
3
a 2

3
8x 4  3 27x 4
d. 3 6 5 10
2
f.
2

3 7 2 3 7

5. Rationalize the denominator. Simplify your answers.
a.
1
2
b.
3
4a
b2
c.
3
11  5
x  4
d.
x  2
6. Solve each equation.
a.
3x  1  3
b.
x  x2
c.
5 x  2  3x  8
d.
x 
x 5  5
7. Use scientific notation and the properties of exponents to calculate.
a.
(0.0003)(400)
0.0002
b.
0.0004
8. Solve for a. Simplify your answers.
a. a 2  40
b.
a  3
2
 49
9. Perform the operations. Write your answers in standard form (a + bi).
a.  6  3i    2  i 
b. 5i 1  3i 
c.  2  3i  2  3i 
d.
6
4  2i
e.
1 i
2  3i
10. Find the domain of each of the following radical functions. Write the answer in interval notation.
a. f ( x )  3 x  4
b. f ( x )  1  2 x
c. f ( x )  3 2 x  5
Complex numbers as solutions are possible.
11. Solve by using the even-root property.
 x  4
2
 25
12. Solve by completing the square. x 2  6 x  11  0
13. Solve by completing the square. 2y 2  5y  1  0
14. Solve by using the quadratic formula. 2 x 2  6 x  1  0 .
(simplify your answer)
State the quadratic formula here:
15. Solve by the method of your choice. 4w 2  25  0
16. Find all real solutions. (method of choice) x 4  6 x 2  8  0
17. Find all real solutions. (method of choice) 2x  5 x  2  0
18. Write a quadratic equation (in form ax 2  bx  c  0 ) that has the given pair of solutions.
a. 3, 2
b. 5i, -5i
19. For the equation x 2  5  3 x
a. Find the value of b 2  4ac .
b. Based on your answer to part (a), how many real solutions will the equation have?
20. Graph the solution set and write your answer in interval notation.
a. 2 x 2  5 x  12
b. 5 x  10 x 2  0
c.
x2
 2
x
d.
3x  1
0
x2
21. Determine the line of symmetry, the vertex, the domain, and the range. Graph the function.
a. y  2x 2  3
b. y  ( x  1)2  4
c. y   x  5 
22. Applications: Chapter Test 7 #23-28 (Textbook pg 632).
2
d. y  ( x  4)2  2